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Guedes, Priscila F.S., Lacerda, Marcio J. and Nepomuceno, Erivelton G. (2024) State-feedback control design for polynomial discrete-time systems obtained via second-order Runge-Kutta discretization. In: 7th IFAC Conference on Analysis and Control of Nonlinear Dynamics and Chaos ACNDC 2024, June 5 – 7, 2024, London, UK.
This paper addresses the state-feedback control problem for the class of state-polynomial discrete-time systems. The continuous-time polynomial nonlinear model is discretized by the second-order Runge-Kutta method. The Lyapunov theory and the exponential stability were employed to derive the conditions. The sum of squares formulation was used to check the constraints. Two approaches are presented, the first makes use of the Lyapunov function to recover the gain matrices. While the second formulation allows the design of rational state feedback control gains. We evaluated the impact of the step size used in the discretization process in the results. Numerical experiments were used to illustrate the potential of the proposed technique.
Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0.
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